The people that find this ridiculous have no concept of business.
I find that comical. I've been a small business owner, consultant, and contractor for the better part of two decades. But do go on. ;-)
The super bowl is a business and the act is a business.
With you so far.
The super bowl is a bigger draw than ANY performer out there so, who benefits from the half time show?
Ultimately, the NFL. That's where all the bucks stop.
Major brands pay millions of dollars for a 30 second spot. How much is a 15 minute spot at half time worth?
The NFL doesn't sell ad time. The network airing the Super Bowl - or simulcasting it overseas, etc. - sells the air time. So while what you're saying is true, it's strictly speaking irrelevant.
If an act has new material coming out, they need to get it exposed as much as possible. They could throw $2M on a multi media advertising campaign or they could pay $2M to play at the SB half time show.
Or they could get paid to add to the spectacle, just as everyone else involved, from the beer vendor to the starting quarterback to the line judge, gets paid.
Professionals get paid to practice their profession, like any other professional involved in making an event into a salable commodity.
Of course I'm just pulling those numbers out of my ass. There are highly paid people that do the math on these things. If the company promoting the music sales think they can increase sales by $10M by investing $2M, it's a good decision.
Which, to turn your initial shot about knowing little about business, shows how little you know about the music business. ;-P The record company isn't paying for the tour, the live shows, none of that. Yes, the tour supports the new album (much of the time), but that's not the record company's lookout.
However, what I'm bitching about, at its core, is that the halftime act is a crucial supporter of the whole shebang, just as much as the players, the officials, the stadium staff, all of that. Might as well start charging the teams who take part. Or the referees. Or, or, or...
Pay to play sets a dangerous precedent for musicians everywhere. That's the point.